In recent years, a piezo-resistive type tri-axial acceleration sensor of a semiconductor device using an MEMS (Micro Electro Mechanical Systems) technique is developed as a light weight and small type of a tri-axial acceleration sensor that can be incorporated in a portable apparatus (see, for example, Japanese Patent Laid-Open No. 2003-101033).
In a tri-axial acceleration sensor that detects acceleration and converts the acceleration to a voltage, when sensitivities in respective axial directions are represented as rx, ry, and rz and offsets on respective axes are represented as xo, yo, and zo, outputs x, y, and z of the acceleration sensor with respect to accelerations ax, ay, and az are represented as indicated by the following formula.
                    {                                                            x                =                                                                            r                      x                                        ⁢                                          a                      x                                                        +                                      x                    o                                                                                                                          y                =                                                                            r                      y                                        ⁢                                          a                      y                                                        +                                      y                    o                                                                                                                          z                =                                                                            r                      z                                        ⁢                                          a                      z                                                        +                                      z                    o                                                                                                          [                  Numeral          ⁢                                          ⁢          1                ]            
In general, sensitivities and offsets have fluctuation respectively and, in particular, the fluctuation in offsets cannot be ignored. Moreover, in the case of a piezo-resistive type acceleration sensor, sensitivities and offsets have marked temperature characteristics. In addition, the temperature characteristic of offsets often shows large fluctuation.
In order to solve such problems, the means described below is used in a conventional acceleration measuring device (see, for example, Japanese Patent Laid-Open No. Hei6-331647).
In an adjustment and test process before shipment, sensitivities and offsets are measured in different plural temperature environment such as 0° C., 25° C., and 60° C. and then the measurement data of sensitivities and offsets is stored to the storing means incorporated in the acceleration measuring device such as an EEPROM.
Further an output correction circuit is incorporated in the acceleration measuring device and then fluctuation and temperature characteristics of sensitivities and offsets included in an acceleration sensor output voltage are calculated and corrected based on present temperature data and the stored measurement data when the acceleration measuring device is used.
However, this type of acceleration measuring device in the past has disadvantages described below.
1) The measurement in the different plural temperature atmospheres and the measurement of sensitivities extremely increase the number of steps of test, measurement time, and equipment cost.
2) The calculation of temperature characteristics of sensitivities and offsets in the output correction circuit complicates a circuit configuration and increases cost.
3) It is necessary to increase the number of measurement temperatures and complicate a temperature characteristic calculation portion in the output correction circuit in order to improve accuracy of the calculation of temperature characteristics of sensitivities and offsets. From this point, it is difficult to realize improvement of calculation accuracy.
In the conventional acceleration measuring device, means for solution is disclosed below. (see, for example, Japanese Patent Laid-Open No. 2004-93552).
Every time the acceleration measuring device is used, for example, as shown in FIGS. 7A to 7F, an attitude of an acceleration measuring device 203 are adjusted in six ways to measure output voltages of the tri-axial acceleration sensor 202 such that acceleration detection axial directions of a tri-axial acceleration sensor 202 are parallel to a direction of the gravitational acceleration “g” respectively, and obtain following output voltage data.
x1: x axis measurement value in an attitude in FIG. 7A
x2: x axis measurement value in an attitude in FIG. 7B
y1: y axis measurement value in an attitude in FIG. 7C
y2: y axis measurement value in an attitude in FIG. 7D
z1: z axis measurement value in an attitude in FIG. 7E
z2: z axis measurement value in an attitude in FIG. 7F
Data of sensitivities and offsets necessary for output correction for the tri-axial acceleration sensor are calculated by the following formula.
                    {                                                                                                  r                    x                                    =                                                                                    x                        1                                            -                                              x                        2                                                                                    2                      ⁢                                                                                          ⁢                      g                                                                                                                                                                r                    y                                    =                                                                                    y                        1                                            -                                              y                        2                                                                                    2                      ⁢                                                                                          ⁢                      g                                                                                                                                                                r                    z                                    =                                                                                    z                        1                                            -                                              z                        2                                                                                    2                      ⁢                                                                                          ⁢                      g                                                                                                    ,                      {                                                                                                      x                      o                                        =                                                                                            x                          1                                                +                                                  x                          2                                                                    2                                                                                                                                                              y                      o                                        =                                                                                            y                          1                                                +                                                  y                          2                                                                    2                                                                                                                                                              z                      o                                        =                                                                                            z                          1                                                +                                                  z                          2                                                                    2                                                                                                                              [                  Numeral          ⁢                                          ⁢          2                ]            
However, this type of conventional acceleration measuring device has disadvantages described below.
1) It is always necessary to adjust attitudes of the acceleration measuring device in plural specific directions, respectively. This case is extremely complicated and inconvenient for a user.
2) Moreover, it is difficult for the user to accurately adjust directions while handling the acceleration measurement device by hand. Errors become larger in sensitivities and offsets calculated by the above formula.
There is an acceleration measuring device (see Japanese Patent Laid-Open No. 2005-056597) in which offsets or both of offsets and sensitivities necessary for output correction for a bi-axial or tri-axial acceleration sensor is acquired by repeatedly obtaining output data of the bi-axial or tri-axial acceleration sensor without setting attitudes of the acceleration measuring device in a specific direction.
The acceleration measuring device described in Japanese Patent Laid-Open No. 2005-056597 estimates offsets or both of offsets and sensitivities using acceleration data at the stationary time.
Acceleration “a” can be resolved into dynamic acceleration “k” and gravitational acceleration “g”. Since the gravitational acceleration “g” is constant,|g|2=g2=const=gx2+gy2+gz2  [Numeral 3]
When dynamic acceleration is 0 (uniform motion or standstill), if sensitivities of respective axes of an acceleration sensor are the same (r), measurement output values (x, y, z) of the acceleration sensor are distributed on a sphere surface.(x−xo)2+(y−yo)2+(z−zo)2=r2g2  [Numeral 4]
According to the above formula (numeral 4), it is possible to estimate offsets (xo, yo, zo) and sensitivities (r) due to four different measurement points. However, actually, noise is superimposed on outputs of the acceleration sensor. Therefore, it is preferable to estimate offsets and sensitivities using a statistical method described below. With N-set of measured acceleration values (xi, yi, zi, i=1 to N),εi=(xi−xo)2+(yi−yo)2+(zi−zo)2−r2g2  [Numeral 5]
is set. And then offsets and sensitivities that minimize fluctuation in εi are estimated. When the fluctuation index is defined as a sum of squares of εi, offsets and sensitivities are calculated by the following formula:
                                          [                                                                                                      ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  x                        i                                            ⁡                                              (                                                                              x                            i                                                    -                                                      x                            _                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  y                        i                                            ⁡                                              (                                                                              x                            i                                                    -                                                      x                            _                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  z                        i                                            ⁡                                              (                                                                              x                            i                                                    -                                                      x                            _                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  y                        i                                            ⁡                                              (                                                                              x                            i                                                    -                                                      x                            _                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  y                        i                                            ⁡                                              (                                                                              y                            i                                                    -                                                      y                            _                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  z                        i                                            ⁡                                              (                                                                              y                            i                                                    -                                                      y                            _                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  z                        i                                            ⁡                                              (                                                                              x                            i                                                    -                                                      x                            _                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  z                        i                                            ⁡                                              (                                                                              y                            i                                                    -                                                      y                            _                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  z                        i                                            ⁡                                              (                                                                              z                            i                                                    -                                                      z                            _                                                                          )                                                                                                                  ]                    ⁡                      [                                                                                x                    0                                                                                                                    y                    0                                                                                                                    x                    0                                                                        ]                          =                              1            2                    ⁡                      [                                                                                                      ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  (                                                                              x                            i                            2                                                    +                                                      y                            i                            2                                                    +                                                      z                            i                            2                                                                          )                                            ⁢                                              (                                                                              x                            i                                                    -                                                      x                            _                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  (                                                                              x                            i                            2                                                    +                                                      y                            i                            2                                                    +                                                      z                            i                            2                                                                          )                                            ⁢                                              (                                                                              y                            i                                                    -                                                      y                            _                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  (                                                                              x                            i                            2                                                    +                                                      y                            i                            2                                                    +                                                      z                            i                            2                                                                          )                                            ⁢                                              (                                                                              z                            i                                                    -                                                      z                            _                                                                          )                                                                                                                  ]                                              [                  Numeral          ⁢                                          ⁢          6                ]                                                          ⁢                              r            2                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                                                          ⁢                              {                                                                            (                                                                        x                          i                                                -                                                  x                          0                                                                    )                                        2                                    +                                                            (                                                                        y                          i                                                -                                                  y                          0                                                                    )                                        2                                    +                                                            (                                                                        z                          i                                                -                                                  z                          0                                                                    )                                        2                                                  }                                                                        [                  Numeral          ⁢                                          ⁢          7                ]            
Here,
                                          x            _                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                                                          ⁢                              x                i                                                    ,                              y            _                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                                                          ⁢                              y                i                                                    ,                              z            _                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                                                          ⁢                              z                i                                                                        [                  Numeral          ⁢                                          ⁢          8                ]            
When dynamic acceleration is 0 (uniform motion or standstill) and sensitivity is different in the respective axes of the acceleration sensor, measurement output values (x, y, z) are distributed on an ellipsoid.
                                                                        (                                  x                  -                                      x                    o                                                  )                            2                                      r              x              2                                +                                                    (                                  y                  -                                      y                    o                                                  )                            2                                      r              y              2                                +                                                    (                                  z                  -                                      z                    o                                                  )                            2                                      r              z              2                                      =                  g          2                                    [                  Numeral          ⁢                                          ⁢          9                ]            
According to the above formula (Numeral 9), it is possible to estimate offset and sensitivities due to six different measurement points. However, actually, noise is superimposed on outputs of the acceleration sensor. Therefore, it is preferable to estimate offsets and sensitivities using a statistical method described below. With respect to N-set of measured acceleration values (xi, yi, zi, i=1 to N)
                              ɛ          i                =                  X          +                      BY            i                    +                      CZ            i                    +                      DU            i                    +                      EV            i                    +                      FW            i                    -                      G            ⁢                                                  (                                                                                                                              X                        i                                            =                                              x                        i                        2                                                              ,                                                                  Y                        i                                            =                                              y                        i                        2                                                              ,                                                                  Z                        i                                            =                                              z                        i                        2                                                              ,                                                                  U                        i                                            =                                              x                        i                                                              ,                                                                  V                        i                                            =                                              y                        i                                                              ,                                                                                                                                                                  W                        i                                            =                                              z                        i                                                              ,                                          B                      =                                                                        r                          x                          2                                                                          r                          y                          2                                                                                      ,                                          C                      =                                                                        r                          x                          2                                                                          r                          z                          2                                                                                      ,                                          D                      =                                                                        -                          2                                                ⁢                                                                                                  ⁢                                                  x                          0                                                                                      ,                                                                                                                                          E                      =                                                                        -                          2                                                ⁢                                                                              r                            x                            2                                                                                r                            y                            2                                                                          ⁢                                                  y                          0                                                                                      ,                                          F                      =                                                                        -                          2                                                ⁢                                                                              r                            x                            2                                                                                r                            z                            2                                                                          ⁢                                                  z                          0                                                                                      ,                                                                                                                    G                    =                                                                  r                        x                        2                                            -                                              x                        0                        2                                            -                                                                                                    r                            x                            2                                                                                r                            y                            2                                                                          ⁢                                                  y                          0                          2                                                                    -                                                                                                    r                            x                            2                                                                                r                            z                            2                                                                          ⁢                                                  z                          0                          2                                                                                                                                          )                                              [                  Numeral          ⁢                                          ⁢          10                ]            
is set. And then offsets and sensitivities that minimize fluctuation in εi are estimated. When the fluctuation is defined as a sum of squares of εi, B, C, D, E, F, and G are calculated by the following formula;
                                          [                                                                                                      ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Y                        i                                            ⁡                                              (                                                                              Y                            i                                                    -                                                      Y                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Y                        i                                            ⁡                                              (                                                                              Z                            i                                                    -                                                      Z                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Y                        i                                            ⁡                                              (                                                                              U                            i                                                    -                                                      U                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Y                        i                                            ⁡                                              (                                                                              V                            i                                                    -                                                      V                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Y                        i                                            ⁡                                              (                                                                              W                            i                                                    -                                                      W                            ^                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Z                        i                                            ⁡                                              (                                                                              Y                            i                                                    -                                                      Y                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Z                        i                                            ⁡                                              (                                                                              Z                            i                                                    -                                                      Z                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Z                        i                                            ⁡                                              (                                                                              U                            i                                                    -                                                      U                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Z                        i                                            ⁡                                              (                                                                              V                            i                                                    -                                                      V                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Z                        i                                            ⁡                                              (                                                                              W                            i                                                    -                                                      W                            ^                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                  U                        i                                            ⁡                                              (                                                                              Y                            i                                                    -                                                      Y                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  U                        i                                            ⁡                                              (                                                                              Z                            i                                                    -                                                      Z                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  U                        i                                            ⁡                                              (                                                                              U                            i                                                    -                                                      U                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  U                        i                                            ⁡                                              (                                                                              V                            i                                                    -                                                      V                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  U                        i                                            ⁡                                              (                                                                              W                            i                                                    -                                                      W                            ^                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                  V                        i                                            ⁡                                              (                                                                              Y                            i                                                    -                                                      Y                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  V                        i                                            ⁡                                              (                                                                              Z                            i                                                    -                                                      Z                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  V                        i                                            ⁡                                              (                                                                              U                            i                                                    -                                                      U                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  V                        i                                            ⁡                                              (                                                                              V                            i                                                    -                                                      V                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  V                        i                                            ⁡                                              (                                                                              W                            i                                                    -                                                      W                            ^                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                  W                        i                                            ⁡                                              (                                                                              Y                            i                                                    -                                                      Y                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  W                        i                                            ⁡                                              (                                                                              Z                            i                                                    -                                                      Z                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  W                        i                                            ⁡                                              (                                                                              U                            i                                                    -                                                      U                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  W                        i                                            ⁡                                              (                                                                              V                            i                                                    -                                                      V                            ^                                                                          )                                                                                                                                                        ∑                                              i                        =                        1                                            N                                        ⁢                                                                  W                        i                                            ⁡                                              (                                                                              W                            i                                                    -                                                      W                            ^                                                                          )                                                                                                                  ]                    ⁡                      [                                                            B                                                                              C                                                                              D                                                                              E                                                                              F                                                      ]                          =                  -                      [                                                                                                      ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Y                        i                                            ⁡                                              (                                                                              X                            i                                                    -                                                      X                            ^                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                  Z                        i                                            ⁡                                              (                                                                              X                            i                                                    -                                                      X                            ^                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                  U                        i                                            ⁡                                              (                                                                              X                            i                                                    -                                                      X                            ^                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                  V                        i                                            ⁡                                              (                                                                              X                            i                                                    -                                                      X                            ^                                                                          )                                                                                                                                                                                    ∑                                              i                        =                        1                                            N                                        ⁢                                                                                  ⁢                                                                  W                        i                                            ⁡                                              (                                                                              X                            i                                                    -                                                      X                            ^                                                                          )                                                                                                                  ]                                              [                  Numeral          ⁢                                          ⁢          11                ]                                                          ⁢                  G          =                                    X              _                        +                          B              ⁢                              Y                _                                      +                          C              ⁢                              Z                _                                      +                          D              ⁢                              U                _                                      +                          E              ⁢                              V                _                                      +                          F              ⁢                              W                _                                                                        [                  Numeral          ⁢                                          ⁢          12                ]            
Here,
                                          X            _                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                              X                i                                                    ,                              Y            _                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                              Y                i                                                    ,                              Z            _                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                              Z                i                                                    ,                                  ⁢                              U            _                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                              U                i                                                    ,                              V            _                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                              V                i                                                    ,                              W            _                    =                                    1              N                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                              W                i                                                                        [                  Numeral          ⁢                                          ⁢          3                ]            
After B, C, D, E, F, and G are calculated, offsets and sensitivities are calculated by the following equation:
                                          x            0                    =                      -                          D              2                                      ,                              y            0                    =                      -                          E                              2                ⁢                                                                  ⁢                B                                                    ,                              z            0                    =                      -                          F                              2                ⁢                                                                  ⁢                C                                                    ,                                  ⁢                              r            x            2                    =                      G            +                          x              0              2                        +                          By              0              2                        +                          Cz              0              2                                      ,                              r            y            2                    =                                    r              x              2                        B                          ,                              r            z            2                    =                                    r              x              2                        C                                              [                  Numeral          ⁢                                          ⁢          14                ]            Patent Document 1: Japanese Patent Laid-Open No. 2003-101033Patent Document 2: Japanese Patent Laid-Open No. 6-331647Patent Document 3: Japanese Patent Laid-Open No. 2004-93552Patent Document 4: Japanese Patent Application No. 2005-056597